# Answer to Question #13813 in Calculus for Alyssa Jennings

Question #13813

I need steps to follow as well, please.

f(x) = x-4

g(x)= 3x^2

find (fog)(x) and (gof)(x)

Detailed expanation

f(x) = x-4

g(x)= 3x^2

find (fog)(x) and (gof)(x)

Detailed expanation

Expert's answer

We're dealing with function composition which is the application of one function to the results of another. It's defined as

(

So (fog)(x)=f(g(x))=g(x)-2=3x^2-4

Here to find the required composition we place expression for g instead of x in the expression for f.

Similarly (gof)(x)=g(f(x))=3f(x)^2=3(x-4)^2

(

*g*∘*f*)(*x*) =*g*(*f*(*x*))So (fog)(x)=f(g(x))=g(x)-2=3x^2-4

Here to find the required composition we place expression for g instead of x in the expression for f.

Similarly (gof)(x)=g(f(x))=3f(x)^2=3(x-4)^2

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